function [x,y,K] = posttransfo(x,y,prep,K,~)
% [xp,yp] = posttransfo(x,y,prep,K)
%
% POSTTRANSFO  Transforms (x,y) from internal SeDuMi format into original
%   user format.
%
% **********  INTERNAL FUNCTION OF SEDUMI **********
%
% See also sedumi

% Nearly complete rewrite
% Copyright (c) 2013 Michael C. Grant
%
% This file is part of SeDuMi 1.1 by Imre Polik and Oleksandr Romanko
% Copyright (C) 2005 McMaster University, Hamilton, CANADA  (since 1.1)
%
% Copyright (C) 2001 Jos F. Sturm (up to 1.05R5)
%   Dept. Econometrics & O.R., Tilburg University, the Netherlands.
%   Supported by the Netherlands Organization for Scientific Research (NWO).
%
% Affiliation SeDuMi 1.03 and 1.04Beta (2000):
%   Dept. Quantitative Economics, Maastricht University, the Netherlands.
%
% Affiliations up to SeDuMi 1.02 (AUG1998):
%   CRL, McMaster University, Canada.
%   Supported by the Netherlands Organization for Scientific Research (NWO).
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
% 02110-1301, USA

% This routine is significantly simpler than before, because most of the
% heavy lifting has been accomplished by the QR matrix.
K.l = K.l - 1;
x = (x'*prep.QR)';
if ~isempty(K.ycomplex)
    ylen = length(y) - length(K.ycomplex);
    y = y(1:ylen) + 1j * sparse(K.ycomplex,1,y(ylen+1:length(y)),ylen,1);
end
if nnz(x) / numel(x) < 1/2
    x = sparse(x);
end
